Re: More complex numbers than reals?

Chris M. Thomasson wrote:

Are there "more" complex numbers than reals? It seems so, every real has
its y, or imaginary, component set to zero. Therefore for each real
there is an infinity of infinite embedding's for it wrt any real with a
non-zero y axis? Fair enough, or really dumb? A little stupid? What do
you think?

No.  You could draw a Hilbert curve (or any other space-filling curve) on
a square of the complex plane and then tile it around in a spiral to fill
up the rest of the plane.  Then, you connect up all the ends of those
tiles together and pull on the ends of the curve to stretch it out to form
a line that is as infinite as the real number line.



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